The Puzzle of Oct 22, 2011: A farmer has a 40 lb stone that he uses to measure out bales of hay on a 2 sided balance. He loans it to a friend who accidentally breaks it into 4 pieces. Instead of being angry, the farmer is quite happy. He says to the friend, "You managed to break it into just the right 4 pieces that will now let me weigh any weight between 1 and 40." What are the weights of the 4 pieces?

I propose a second challenge: Are there any posters out there with black belts in Google who can find the solution on the internet? The solution is out there.

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## Comments

Why do you NEED google...How about trying to figure it out on your own...

why does Google keep sending me back to cartalk's page when I search?No...it's probably because cartalk is the only thing google can find on the subject.

I did before I googled.Here's a hint....Hopefully it won't give it away.

Suppose you have 3 stones (5lb, 2lb and a 1lb).

Someone brings in a bag of rice...that he says weighs 4lbs.

How would you weigh it? The challenge is you don't have any combination of stones that weigh 4lbs.

Here's how you'd do it.

Put the bag of rice on one side of the scale..and the 5lb stone on the other....Then add the 1lb stone to the side of scale with the rice....If they balance out..then the bag of rice weighs 4lbs.

That is not a hint at all, because one would still be left in choosing, presumably at random, four weights that could be placed on a balance scale to balance any integer weight between 1 and 40 lbs.

Warning! Hint given below.Proceed more methodically. Find the smallest stone, of weight

W(2)lbs, that can be broken intotwoparts, such that the two smaller broken pieces can balance any weight from1toW(2)lbs. Then proceed to find the next smallest weight,W(3)lbs, that can be broken in tothreepieces, etc. ... and proceed in that fashion to find the smallest weight,W(n)lbs, that can be broken intonpieces that can be used to balance any weight from1toW(n)lbs. (Obviously,W(4) = 40lbs.) By solving initially then=2problem, a general solution will emerge.Sorry mechaniker...That's the best hint I can give you without actually telling you the answer...You should be able to figure out the rest.

If I said "I can't believe i didn't remember base three from elementary school", would I be giving it away? I forgive the recycled puzzler since I forgot what I learned over Summer alsoI figured out the answer a while ago......And I do know how what base 3 is....And if you remember what Base 3 is...then this is a MAJOR clue.